{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据处理与统计模块\n",
    "numpy（np）、pandas（pd）：用于高效的数值计算和数据结构处理，是数据科学领域的基础工具。\n",
    "scipy.stats（stats）、scipy：提供统计分析、科学计算的功能，如假设检验、优化等。\n",
    "statsmodels.formula.api（smf）：用于执行普通最小二乘法（OLS）回归等统计建模。\n",
    "时间与数据库模块\n",
    "datetime：处理日期和时间数据。\n",
    "pymysql（被注释）：用于连接和操作 MySQL 数据库。\n",
    "绘图模块\n",
    "matplotlib系列（style、pyplot（plt）、dates（mdates）、font_manager）：用于数据可视化，包括设置绘图风格、绘制图表、处理日期格式、配置中文字体等。\n",
    "pylab（mpl）：结合了numpy和matplotlib的功能，方便绘图操作。\n",
    "Jupyter Notebook 环境配置模块\n",
    "IPython.core.interactiveshell（InteractiveShell）：设置 Jupyter Notebook 中每个节点的输出模式为 “all”，即显示所有运行结果。\n",
    "pandas的set_option：设置pandas数据框的显示行数和列数为无限制，便于查看完整数据。\n",
    "%matplotlib inline和%config：设置在 Jupyter Notebook 中内嵌显示图表，并将图表格式设置为 SVG（矢量图格式，保证清晰度）。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 股票市场回报率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>ret_e</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>Q</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.036554</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>0.029624</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.021860</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>0.014930</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>-0.060425</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>-0.067355</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>-0.031449</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>-0.038100</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.005375</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>-0.000717</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>-0.033685</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.034803</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.227078</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.225960</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.070220</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.069102</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.045312</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.044194</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>-0.040799</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.041917</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR  MarketR_e   rfmonth       ret     ret_e  marketret3  \\\n",
       "month                                                                       \n",
       "1991-01-31  0.029998   0.036554  0.006930  0.023068  0.029624   -0.084127   \n",
       "1991-02-28  0.010203   0.021860  0.006930  0.003273  0.014930   -0.183573   \n",
       "1991-03-31 -0.099663  -0.060425  0.006930 -0.106593 -0.067355   -0.252928   \n",
       "1991-04-30 -0.079652  -0.031449  0.006651 -0.086303 -0.038100   -0.234776   \n",
       "1991-05-31 -0.074521   0.005375  0.006092 -0.080613 -0.000717   -0.236294   \n",
       "...              ...        ...       ...       ...       ...         ...   \n",
       "2024-08-31 -0.031468  -0.033685  0.001118 -0.032586 -0.034803    0.151050   \n",
       "2024-09-30  0.195992   0.227078  0.001118  0.194874  0.225960    0.200147   \n",
       "2024-10-31 -0.003409   0.070220  0.001118 -0.004527  0.069102    0.000228   \n",
       "2024-11-30  0.009724   0.045312  0.001118  0.008606  0.044194         NaN   \n",
       "2024-12-31 -0.002679  -0.040799  0.001118 -0.003797 -0.041917         NaN   \n",
       "\n",
       "            marketret6  marketret12        Q  \n",
       "month                                         \n",
       "1991-01-31   -0.305662     0.254049  1991 Q1  \n",
       "1991-02-28   -0.384745     0.241492  1991 Q1  \n",
       "1991-03-31   -0.445049     0.288857  1991 Q1  \n",
       "1991-04-30   -0.394937     0.691749  1991 Q2  \n",
       "1991-05-31    0.181673     1.542701  1991 Q2  \n",
       "...                ...          ...      ...  \n",
       "2024-08-31         NaN          NaN  2024 Q3  \n",
       "2024-09-30         NaN          NaN  2024 Q3  \n",
       "2024-10-31         NaN          NaN  2024 Q4  \n",
       "2024-11-30         NaN          NaN  2024 Q4  \n",
       "2024-12-31         NaN          NaN  2024 Q4  \n",
       "\n",
       "[408 rows x 9 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas.tseries.offsets import MonthEnd # 月末\n",
    "Market_ret = pd.read_csv('datasets/Marketret_mon_stock2024.csv')\n",
    "Market_ret['month'] = pd.to_datetime(Market_ret['month'], format='%b %Y') + MonthEnd(0)\n",
    "Market_ret.set_index('month', inplace=True)\n",
    "Market_ret.sort_index(inplace=True)\n",
    "Market_ret = Market_ret.drop(columns=['Unnamed: 0'])\n",
    "Market_ret                              "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1987-01-31</th>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-02-28</th>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-03-31</th>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-04-30</th>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-05-31</th>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-03-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-04-30</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-05-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-06-30</th>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-07-31</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>463 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            cpi\n",
       "month          \n",
       "1987-01-31  5.1\n",
       "1987-02-28  5.4\n",
       "1987-03-31  5.8\n",
       "1987-04-30  6.7\n",
       "1987-05-31  7.6\n",
       "...         ...\n",
       "2025-03-31 -0.1\n",
       "2025-04-30 -0.1\n",
       "2025-05-31 -0.1\n",
       "2025-06-30  0.1\n",
       "2025-07-31  0.0\n",
       "\n",
       "[463 rows x 1 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inflation = pd.read_csv('datasets/inflation.csv')\n",
    "inflation['month'] = pd.to_datetime(inflation['month'],format='%Y/%m/%d')\n",
    "inflation.set_index('month',inplace=True)\n",
    "inflation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "price_dividend = pd.read_csv('datasets/Price_dividend_mon2024.csv')\n",
    "price_dividend['month'] = pd.date_range(start='1990-12-31', end='2024-12-31', freq='ME')\n",
    "price_dividend.set_index('month', inplace=True)\n",
    "price_dividend.sort_index(inplace=True)\n",
    "price_dividend = price_dividend.drop(columns=['Unnamed: 0'])\n",
    "\n",
    "price_earning = pd.read_csv('datasets/Price_earnings_mon2024.csv')\n",
    "price_earning['month'] = pd.date_range(start='1991-01-31', end='2024-12-31', freq='ME')\n",
    "price_earning.set_index('month', inplace=True)\n",
    "price_earning.sort_index(inplace=True)\n",
    "\n",
    "price_bookvalue = pd.read_csv('datasets/Price_bookvalue_mon2024.csv')\n",
    "price_bookvalue['month'] = pd.date_range(start='1990-12-31', end='2024-12-31', freq='ME')\n",
    "price_bookvalue.set_index('month', inplace=True)\n",
    "price_bookvalue.sort_index(inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以通过封装函数来避免重复代码，提升可读性和可维护性：\n",
    "def process_fin_data(file_path, start_date, end_date):\n",
    "    \"\"\"处理金融数据的通用函数：读取、设置日期列、索引、排序、删除冗余列\"\"\"\n",
    "    df = pd.read_csv(file_path)\n",
    "    df['month'] = pd.date_range(start=start_date, end=end_date, freq='ME')\n",
    "    df.set_index('month', inplace=True)\n",
    "    df.sort_index(inplace=True)\n",
    "    df = df.drop(columns=['Unnamed: 0'])\n",
    "    return df\n",
    "\n",
    "# 分别处理三个数据集\n",
    "price_dividend = process_fin_data('datasets/Price_dividend_mon2024.csv', '1990-12-31', '2024-12-31')\n",
    "price_earning = process_fin_data('datasets/Price_earnings_mon2024.csv', '1991-01-31', '2024-12-31')\n",
    "price_bookvalue = process_fin_data('datasets/Price_bookvalue_mon2024.csv', '1990-12-31', '2024-12-31')\n",
    "这样的优化让代码结构更清晰，后续若新增同类数据文件，只需调用 process_fin_data 函数即可，减少了重复逻辑的维护成本。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 月度数据的预测\n",
    "\n",
    "A simple linear regression of an asset return on one or a few lagged predictors of interest is the most popular econometric approach for testing for return predictability. For simplicity, consider a univariate predictive regression of the period- $(t + 1)$ stock market return $r_{t+1}$ on a single predictor variable $x_t$:\n",
    "$$\n",
    "r_{t+1}=\\alpha+\\beta x_{t}+\\varepsilon_{t+1}\n",
    "$$\n",
    "where $\\varepsilon_{t+1}$ is a zero-mean, unpredictable disturbance term. When $x_t$ is the inflation rate, dividend yield, book-to-price ratio, or turnover. Many researchers find that $\\beta$ is significantly different from zero; that is, there is in-sample evidence of stock market return predictability.\n",
    "\n",
    "* H0:$\\beta = 0$\n",
    "* H1:$\\beta \\ne 0$(我们需要通过理论分析，得出$\\beta$的符号)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 股权溢价之谜 和 消费基础的资产定价\n",
    "\n",
    "$$\n",
    "r_{t} = \\gamma E_{t-1}(cov(r,\\Delta c))\n",
    "$$\n",
    "\n",
    "其中:\n",
    "- $\\Delta c$ 是消费增长率\n",
    "- $cov(r,\\Delta c)$ 是资产收益率与消费增长率的协方差\n",
    "- 这个关系式来源于消费基础资产定价模型(C-CAPM)\n",
    "- 历史数据显示美国股权溢价约为 6-8%\n",
    "\n",
    "### 股权溢价之谜 (Equity Premium Puzzle)\n",
    "\n",
    "**定义**: Mehra and Prescott (1985) 发现,用标准的经济模型很难解释历史上观察到的高股权溢价(股票收益率相对于无风险利率的超额收益)。\n",
    "\n",
    "要解释历史上的高股权溢价,需要:\n",
    "1. **非常高的风险厌恶系数** $\\gamma$ (远超过合理的经济学估计值 2-10)\n",
    "2. 或者**消费增长与股票收益的协方差非常高**(但实际数据中并非如此)\n",
    "\n",
    "#### 可能的解释\n",
    "\n",
    "1. **有限参与** (Limited Participation): 并非所有投资者都参与股票市场\n",
    "2. **损失厌恶** (Loss Aversion): 投资者对损失比对收益更敏感\n",
    "3. **灾难风险** (Rare Disaster Risk): 小概率极端事件的担忧 (Barro, 2006)\n",
    "4. **长期风险** (Long-run Risk): 消费增长的持续性波动 (Bansal-Yaron, 2004)\n",
    "\n",
    "- **消费数据**：宏观消费数据通常是按季度或年度发布的，存在显著的测量误差，并且会经历多次修正。这使得用它来检验高频的金融市场现象变得非常困难 。\n",
    "- **市场回报数据**：股票市场的回报数据质量非常高，可以精确到每日甚至更高频率，且不存在修正问题。\n",
    "\n",
    "### 理论溯源：跨期资本资产定价模型 (ICAPM)\n",
    "\n",
    "该模型的理论基石是罗伯特·默顿（Robert Merton）在1973年提出的跨期资本资产定价模型（Intertemporal Capital Asset Pricing Model, ICAPM）。ICAPM的核心观点是，在一个动态的多时期世界里，理性的、风险规避的投资者不仅会因为承担当前的系统性风险而要求补偿，还会因为未来投资机会的变化（例如未来利率、市场波动率的变化）而要求额外的风险溢价。\n",
    "\n",
    "ICAPM的一个关键推论是，市场组合的预期超额收益（Expected Excess Return）与它的条件方差（Conditional Variance）之间存在线性的正相关关系。条件方差衡量了在当前信息下对下一期市场波动性的预期，是市场风险的直接度量。因此，ICAPM预测了如下关系：\n",
    "\n",
    "$$\n",
    "E_{t-1}(r_{M,t}) = \\gamma \\cdot E_{t-1} \\left (\\sigma_{M,t}^2 \\right)\n",
    "$$\n",
    "\n",
    "其中：\n",
    "-   $E_{t-1}(r_{M,t})$ 是在 $t-1$ 时点对市场组合在 $t$ 时期的超额收益的期望。\n",
    "-   $E_{t-1} \\left (\\sigma_{M,t}^2 \\right)$ 是在 $t-1$ 时点对市场组合在 $t$ 时期的风险的期望。\n",
    "-   $\\gamma$ 代表了市场投资者的平均相对风险厌恶系数，也被称为“风险的价格”，它衡量了投资者为承担单位市场风险所要求的额外预期收益。\n",
    "\n",
    "\n",
    "### 实证检验\n",
    "\n",
    "本节通过检验以下关系:\n",
    "$$\n",
    "r_{t+1} = \\alpha + \\beta \\cdot RV_t + \\varepsilon_{t+1}\n",
    "$$\n",
    "\n",
    "其中 $RV_t$ 是已实现波动率(realized variance),作为条件方差 $E_t(\\sigma^2_{t+1})$ 的估计。\n",
    "\n",
    "**理论预期**: 如果 ICAPM 成立,应该有 $\\beta > 0$ 且显著。\n",
    "\n",
    "然而，在实际操作中：\n",
    "\n",
    "$$\n",
    "RV_t(k)=\\sum_{d=1}^{D_t} r_{d, t}^2+2 \\sum_{j=1}^k \\sum_{d=j+1}^{D_t} r_{d, t} r_{d-j, t}\n",
    "$$\n",
    "\n",
    "### 计量实现：均值内ARCH (ARCH-in-Mean) 模型\n",
    "\n",
    "为了在实际数据中检验ICAPM所预测的风险-收益关系，需要一个能够同时处理收益率均值和时变波动率（即异方差性）的计量模型。罗伯特·恩格尔（Robert Engle）等人于1987年提出的均值内自回归条件异方差模型（ARCH-in-Mean, ARCH-M）正是为此而生。\n",
    "\n",
    "ARCH-M模型是对早期ARCH模型的扩展。标准的ARCH及后来更具一般性的GARCH模型，主要用于刻画金融时间序列中普遍存在的波动率聚类现象（volatility clustering），即高波动率时期和低波动率时期会各自聚集出现。这些模型的核心是建立一个独立的方程来描述条件方差 $\\sigma_t^2$ 如何随时间变化，通常是过去残差平方和过去方差的函数。\n",
    "\n",
    "ARCH-M模型的创新之处在于，它将条件方差（或条件标准差）作为一个解释变量引入到资产收益率的均值方程中。这使得研究者可以直接估计和检验风险（由 $\\sigma_t^2$ 度量）对预期收益（$E_{t-1}(r_t)$）的影响。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "r_t & =\\mu+c \\sigma_t^2+a_t  \\\\\n",
    "\\sigma_t^2 & =\\alpha_0+\\alpha_1 a_{t-1}^2+\\beta_1 \\sigma_{t-1}^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "### 核心参数的经济学含义\n",
    "\n",
    "参数 $\\gamma$ 的估计结果至关重要。\n",
    "-   如果 $\\gamma$ 显著为正，则支持了经典的金融理论，即存在正向的风险收益权衡关系：投资者在预期到未来市场波动性将加剧时，会要求更高的预期回报作为承担更高风险的补偿。\n",
    "-   如果 $\\gamma$ 不显著或为负，则对该理论提出了挑战。\n",
    "\n",
    "值得注意的是，尽管理论上 $\\gamma$ 应该为正，但在不同市场、不同时期和不同模型设定下的实证研究结果却并不一致，一些研究发现了显著为正的关系，而另一些研究则得到了不显著甚至为负的结果。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>month</th>\n",
       "      <th>Q</th>\n",
       "      <th>rfday</th>\n",
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       "      <th>pos_er</th>\n",
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       "      <th>pos_er2</th>\n",
       "      <th>pos_er3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>0.050067</td>\n",
       "      <td>0.752547</td>\n",
       "      <td>12 1990</td>\n",
       "      <td>1990 Q4</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>0.039671</td>\n",
       "      <td>67.771445</td>\n",
       "      <td>12 1990</td>\n",
       "      <td>1990 Q4</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>0.049380</td>\n",
       "      <td>0.049638</td>\n",
       "      <td>12 1990</td>\n",
       "      <td>1990 Q4</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>0.049938</td>\n",
       "      <td>0.050022</td>\n",
       "      <td>12 1990</td>\n",
       "      <td>1990 Q4</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.049711</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.049711</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-26</th>\n",
       "      <td>0.050151</td>\n",
       "      <td>0.050151</td>\n",
       "      <td>12 1990</td>\n",
       "      <td>1990 Q4</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.049924</td>\n",
       "      <td>0.049711</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
       "      <td>0.049840</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.049924</td>\n",
       "      <td>0.049711</td>\n",
       "      <td>0.049153</td>\n",
       "      <td>0.039444</td>\n",
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       "      <th>2024-12-25</th>\n",
       "      <td>-0.004361</td>\n",
       "      <td>-0.019226</td>\n",
       "      <td>12 2024</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.000037</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>2024-12-26</th>\n",
       "      <td>0.002969</td>\n",
       "      <td>0.011729</td>\n",
       "      <td>12 2024</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>0.002932</td>\n",
       "      <td>-0.004398</td>\n",
       "      <td>0.012003</td>\n",
       "      <td>-0.009967</td>\n",
       "      <td>-0.000314</td>\n",
       "      <td>0.000000</td>\n",
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       "      <td>0.000000</td>\n",
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       "      <td>0.002932</td>\n",
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       "      <td>0.000000</td>\n",
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       "      <th>2024-12-27</th>\n",
       "      <td>0.002119</td>\n",
       "      <td>0.008489</td>\n",
       "      <td>12 2024</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>0.002082</td>\n",
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       "      <th>2024-12-30</th>\n",
       "      <td>0.000660</td>\n",
       "      <td>-0.008647</td>\n",
       "      <td>12 2024</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>0.000623</td>\n",
       "      <td>0.002082</td>\n",
       "      <td>0.002932</td>\n",
       "      <td>-0.004398</td>\n",
       "      <td>0.012003</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.004398</td>\n",
       "      <td>0.000623</td>\n",
       "      <td>0.002082</td>\n",
       "      <td>0.002932</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.018452</td>\n",
       "      <td>-0.024026</td>\n",
       "      <td>12 2024</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.000037</td>\n",
       "      <td>-0.018489</td>\n",
       "      <td>0.000623</td>\n",
       "      <td>0.002082</td>\n",
       "      <td>0.002932</td>\n",
       "      <td>-0.004398</td>\n",
       "      <td>-0.018489</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000623</td>\n",
       "      <td>0.002082</td>\n",
       "      <td>0.002932</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8361 rows × 18 columns</p>\n",
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      ],
      "text/plain": [
       "             MarketR  MarketR_e    month        Q     rfday        er  \\\n",
       "Day                                                                     \n",
       "1990-12-20  0.050067   0.752547  12 1990  1990 Q4  0.000227  0.049840   \n",
       "1990-12-21  0.039671  67.771445  12 1990  1990 Q4  0.000227  0.039444   \n",
       "1990-12-24  0.049380   0.049638  12 1990  1990 Q4  0.000227  0.049153   \n",
       "1990-12-25  0.049938   0.050022  12 1990  1990 Q4  0.000227  0.049711   \n",
       "1990-12-26  0.050151   0.050151  12 1990  1990 Q4  0.000227  0.049924   \n",
       "...              ...        ...      ...      ...       ...       ...   \n",
       "2024-12-25 -0.004361  -0.019226  12 2024  2024 Q4  0.000037 -0.004398   \n",
       "2024-12-26  0.002969   0.011729  12 2024  2024 Q4  0.000037  0.002932   \n",
       "2024-12-27  0.002119   0.008489  12 2024  2024 Q4  0.000037  0.002082   \n",
       "2024-12-30  0.000660  -0.008647  12 2024  2024 Q4  0.000037  0.000623   \n",
       "2024-12-31 -0.018452  -0.024026  12 2024  2024 Q4  0.000037 -0.018489   \n",
       "\n",
       "                 er1       er2       er3       er4    neg_er   neg_er1  \\\n",
       "Day                                                                      \n",
       "1990-12-20       NaN       NaN       NaN       NaN  0.000000       NaN   \n",
       "1990-12-21  0.049840       NaN       NaN       NaN  0.000000  0.000000   \n",
       "1990-12-24  0.039444  0.049840       NaN       NaN  0.000000  0.000000   \n",
       "1990-12-25  0.049153  0.039444  0.049840       NaN  0.000000  0.000000   \n",
       "1990-12-26  0.049711  0.049153  0.039444  0.049840  0.000000  0.000000   \n",
       "...              ...       ...       ...       ...       ...       ...   \n",
       "2024-12-25  0.012003 -0.009967 -0.000314 -0.001943 -0.004398  0.000000   \n",
       "2024-12-26 -0.004398  0.012003 -0.009967 -0.000314  0.000000 -0.004398   \n",
       "2024-12-27  0.002932 -0.004398  0.012003 -0.009967  0.000000  0.000000   \n",
       "2024-12-30  0.002082  0.002932 -0.004398  0.012003  0.000000  0.000000   \n",
       "2024-12-31  0.000623  0.002082  0.002932 -0.004398 -0.018489  0.000000   \n",
       "\n",
       "             neg_er2   neg_er3    pos_er   pos_er1   pos_er2   pos_er3  \n",
       "Day                                                                     \n",
       "1990-12-20       NaN       NaN  0.049840       NaN       NaN       NaN  \n",
       "1990-12-21       NaN       NaN  0.039444  0.049840       NaN       NaN  \n",
       "1990-12-24  0.000000       NaN  0.049153  0.039444  0.049840       NaN  \n",
       "1990-12-25  0.000000  0.000000  0.049711  0.049153  0.039444  0.049840  \n",
       "1990-12-26  0.000000  0.000000  0.049924  0.049711  0.049153  0.039444  \n",
       "...              ...       ...       ...       ...       ...       ...  \n",
       "2024-12-25 -0.009967 -0.000314  0.000000  0.012003  0.000000  0.000000  \n",
       "2024-12-26  0.000000 -0.009967  0.002932  0.000000  0.012003  0.000000  \n",
       "2024-12-27 -0.004398  0.000000  0.002082  0.002932  0.000000  0.012003  \n",
       "2024-12-30  0.000000 -0.004398  0.000623  0.002082  0.002932  0.000000  \n",
       "2024-12-31  0.000000  0.000000  0.000000  0.000623  0.002082  0.002932  \n",
       "\n",
       "[8361 rows x 18 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Market_ret_day = pd.read_excel('datasets/Marketret_day_stock2024.xlsx')\n",
    "Market_ret_day['Day'] = pd.to_datetime(Market_ret_day['Day'],format='%Y-%m-%d')\n",
    "Market_ret_day.set_index('Day',inplace=True)\n",
    "Market_ret_day.sort_index(inplace=True)\n",
    "Market_ret_day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>0.011709</td>\n",
       "      <td>0.030732</td>\n",
       "      <td>0.046608</td>\n",
       "      <td>0.058424</td>\n",
       "      <td>0.000395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>0.000030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>0.000014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>409 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RV       RV1       RV2       RV3       var\n",
       "month                                                       \n",
       "1990-12-31  0.011709  0.030732  0.046608  0.058424  0.000395\n",
       "1991-01-31  0.000690  0.001566  0.002593  0.003461  0.000030\n",
       "1991-02-28  0.000418  0.000707  0.000853  0.000763  0.000024\n",
       "1991-03-31  0.001229  0.002925  0.004650  0.006369  0.000014\n",
       "1991-04-30  0.000855  0.001973  0.003364  0.004531  0.000010\n",
       "...              ...       ...       ...       ...       ...\n",
       "2024-08-31  0.000881  0.000823  0.000487  0.000487  0.000040\n",
       "2024-09-30  0.012481  0.023868  0.034838  0.041347  0.000593\n",
       "2024-10-31  0.011652  0.007954  0.006707  0.006707  0.000685\n",
       "2024-11-30  0.004019  0.004118  0.005938  0.003775  0.000201\n",
       "2024-12-31  0.001713  0.001517  0.001623  0.001167  0.000082\n",
       "\n",
       "[409 rows x 5 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate monthly realized variance (RV) by summing squared excess returns\n",
    "Market_variance = Market_ret_day.resample('ME').apply(lambda df: pd.Series({\n",
    "    'RV': (df['er']**2).sum(),\n",
    "    'RV1': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum(),\n",
    "    'RV2': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum(),\n",
    "    'RV3': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum() + 2*(df['er']*df['er3']).sum()\n",
    "}))\n",
    "\n",
    "Market_variance['var'] = Market_ret_day.resample('ME')['er'].var()\n",
    "Market_variance.index.name = 'month'\n",
    "\n",
    "# if RV3 <0, set to RV2 if RV2 <0, set to RV1 if RV1 <0, set to RV\n",
    "Market_variance['RV1'] = Market_variance['RV1'].where(Market_variance['RV1']>=0, Market_variance['RV'])\n",
    "Market_variance['RV2'] = Market_variance['RV2'].where(Market_variance['RV2']>=0, Market_variance['RV1'])\n",
    "Market_variance['RV3'] = Market_variance['RV3'].where(Market_variance['RV3']>=0, Market_variance['RV2'])\n",
    "Market_variance\n",
    "\n",
    "# market_variance <- daily_data[,.(MV = sum(er^2)),by = 'month'] This is R code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过resample('ME')按月末频率聚合日度数据，分别计算RV（日超额收益平方和）、RV1（含一阶交叉项的平方和）、RV2（含二阶交叉项）、RV3（含三阶交叉项）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>0.000030</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.466562</td>\n",
       "      <td>2.080065</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000024</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.501042</td>\n",
       "      <td>1.949285</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.112082</td>\n",
       "      <td>1.560324</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.111121</td>\n",
       "      <td>1.970330</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>3.6</td>\n",
       "      <td>0.000480</td>\n",
       "      <td>0.001262</td>\n",
       "      <td>0.002119</td>\n",
       "      <td>0.002949</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.182871</td>\n",
       "      <td>1.901101</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR   rfmonth       ret  cpi        RV       RV1       RV2  \\\n",
       "month                                                                         \n",
       "1991-01-31  0.029998  0.006930  0.023068  2.2  0.000690  0.001566  0.002593   \n",
       "1991-02-28  0.010203  0.006930  0.003273  1.0  0.000418  0.000707  0.000853   \n",
       "1991-03-31 -0.099663  0.006930 -0.106593  1.6  0.001229  0.002925  0.004650   \n",
       "1991-04-30 -0.079652  0.006651 -0.086303  1.3  0.000855  0.001973  0.003364   \n",
       "1991-05-31 -0.074521  0.006092 -0.080613  3.6  0.000480  0.001262  0.002119   \n",
       "...              ...       ...       ...  ...       ...       ...       ...   \n",
       "2024-08-31 -0.031468  0.001118 -0.032586  0.6  0.000881  0.000823  0.000487   \n",
       "2024-09-30  0.195992  0.001118  0.194874  0.4  0.012481  0.023868  0.034838   \n",
       "2024-10-31 -0.003409  0.001118 -0.004527  0.3  0.011652  0.007954  0.006707   \n",
       "2024-11-30  0.009724  0.001118  0.008606  0.2  0.004019  0.004118  0.005938   \n",
       "2024-12-31 -0.002679  0.001118 -0.003797  0.1  0.001713  0.001517  0.001623   \n",
       "\n",
       "                 RV3       var         pd        pe        pb  marketret3  \\\n",
       "month                                                                       \n",
       "1991-01-31  0.003461  0.000030        NaN  4.466562  2.080065   -0.084127   \n",
       "1991-02-28  0.000763  0.000024        NaN  4.501042  1.949285   -0.183573   \n",
       "1991-03-31  0.006369  0.000014        NaN  4.112082  1.560324   -0.252928   \n",
       "1991-04-30  0.004531  0.000010        NaN  4.111121  1.970330   -0.234776   \n",
       "1991-05-31  0.002949  0.000005        NaN  4.182871  1.901101   -0.236294   \n",
       "...              ...       ...        ...       ...       ...         ...   \n",
       "2024-08-31  0.000487  0.000040  10.728048  2.502897  0.097936    0.151050   \n",
       "2024-09-30  0.041347  0.000593  10.889979  2.675435  0.275764    0.200147   \n",
       "2024-10-31  0.006707  0.000685  10.862945  2.635010  0.254341    0.000228   \n",
       "2024-11-30  0.003775  0.000201  10.858076  2.643930  0.263924         NaN   \n",
       "2024-12-31  0.001167  0.000082  10.842070  2.652927  0.261665         NaN   \n",
       "\n",
       "            marketret6  marketret12  \n",
       "month                                \n",
       "1991-01-31   -0.305662     0.254049  \n",
       "1991-02-28   -0.384745     0.241492  \n",
       "1991-03-31   -0.445049     0.288857  \n",
       "1991-04-30   -0.394937     0.691749  \n",
       "1991-05-31    0.181673     1.542701  \n",
       "...                ...          ...  \n",
       "2024-08-31         NaN          NaN  \n",
       "2024-09-30         NaN          NaN  \n",
       "2024-10-31         NaN          NaN  \n",
       "2024-11-30         NaN          NaN  \n",
       "2024-12-31         NaN          NaN  \n",
       "\n",
       "[408 rows x 15 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data = pd.merge(Market_ret,inflation,on = 'month')\n",
    "reg_data = pd.merge(reg_data,Market_variance,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_dividend,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_earning,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_bookvalue,on = 'month')\n",
    "reg_data = reg_data[['MarketR','rfmonth','ret','cpi','RV','RV1','RV2','RV3','var','pd','pe','pb','marketret3','marketret6','marketret12']]\n",
    "# Output reg_data to reg_data.csv\n",
    "reg_data.to_csv('datasets/reg_data.csv')\n",
    "# Output reg_data to reg_data.xlsx\n",
    "reg_data.to_excel('datasets/reg_data.xlsx')\n",
    "\n",
    "reg_data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 明确列筛选，增强可读性\n",
    "selected_columns = [\n",
    "    'MarketR', 'rfmonth', 'ret', 'cpi', \n",
    "    'RV', 'RV1', 'RV2', 'RV3', 'var', \n",
    "    'pd', 'pe', 'pb', \n",
    "    'marketret3', 'marketret6', 'marketret12'\n",
    "]\n",
    "reg_data = reg_data[selected_columns]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作图 Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
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   ],
   "source": [
    "# 对比RV3和RV var\n",
    "reg_data_plot = reg_data['2000-01':'2024-12'].copy()\n",
    "# Plot the RV3 and var into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(10,5))\n",
    "\n",
    "ax1.plot(reg_data_plot['RV3'],color='blue',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance (RV3)')\n",
    "ax1.set_ylabel('Realized Variance (RV3)',color='blue')\n",
    "ax1.tick_params(axis='y', labelcolor='blue')   \n",
    "ax1.set_title(\"China Stock Market Realized Variance (RV3) and Variance (var)\", fontsize=16)\n",
    "\n",
    "ax1.plot(reg_data_plot['var'],color='green',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Variance (var)')\n",
    "ax1.plot(reg_data_plot['RV'],color='red',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance (RV)')\n",
    "\n",
    "ax1.legend(loc='upper left')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绿色的var整体处于极低水平，几乎贴近 0 轴，说明传统方差在捕捉中国股市波动率时敏感性不足；\n",
    "蓝色RV3和红色RV则波动剧烈，能更直观反映市场的波动率变化。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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       "      <!-- 2010 -->\n",
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       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_13\">\n",
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       "       <use xlink:href=\"#mecee0ed9d4\" x=\"299.808239\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_14\">\n",
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       "       <use xlink:href=\"#mecee0ed9d4\" x=\"320.152657\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mecee0ed9d4\" x=\"340.552813\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
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       "      <!-- 2013 -->\n",
       "      <g transform=\"translate(343.312188 331.968125) rotate(-90) scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-33\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use xlink:href=\"#mecee0ed9d4\" x=\"360.89723\" y=\"299.518125\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 2014 -->\n",
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       "       <use xlink:href=\"#DejaVuSans-32\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-34\" transform=\"translate(190.869141 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_17\">\n",
       "     <g id=\"line2d_17\">\n",
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       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-35\" transform=\"translate(190.869141 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_18\">\n",
       "     <g id=\"line2d_18\">\n",
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       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-36\" transform=\"translate(190.869141 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_19\">\n",
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       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-37\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_20\">\n",
       "     <g id=\"line2d_20\">\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-38\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_21\">\n",
       "     <g id=\"line2d_21\">\n",
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       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(63.623047 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-31\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-39\" transform=\"translate(190.869141 0)\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_22\">\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(127.246094 0)\"/>\n",
       "       <use xlink:href=\"#DejaVuSans-30\" transform=\"translate(190.869141 0)\"/>\n",
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       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_23\">\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(127.246094 0)\"/>\n",
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       "       <use xlink:href=\"#DejaVuSans-32\" transform=\"translate(127.246094 0)\"/>\n",
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       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "reg_data_plot = reg_data['2000-01':'2024-12'].copy()\n",
    "# Plot the China's stock market return and inflation into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(10,5))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(reg_data_plot['ret'],color='red',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='red')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data_plot['RV3'].shift(1),color='blue',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance')\n",
    "\n",
    "ax2.set_ylabel('Realized Variance',color='blue')\n",
    "\n",
    "plt.title('China Stock Market Return and Realized Variance')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "轴ax1绘制股市收益率（ret），颜色为红色，标记为 “o”，线宽 0.8，标记大小 4，线型为实线，标签为 “China Stock Market Return”，并设置 y 轴标签和刻度颜色为红色；同时设置 x 轴日期显示格式为年份，且刻度旋转 90 度。\n",
    "轴ax2（ax1的双轴）绘制滞后一期的已实现方差（RV3.shift(1)），颜色为蓝色，样式同收益率序列，标签为 “Realized Variance”，设置 y 轴标签和刻度颜色为蓝色。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 描述性统计 Summary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    408.00000\n",
       "mean       0.00876\n",
       "std        0.01858\n",
       "min        0.00027\n",
       "25%        0.00189\n",
       "50%        0.00357\n",
       "75%        0.00882\n",
       "max        0.25211\n",
       "Name: RV, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['RV'].describe().round(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(7.734617011548641)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(82.80411751131915)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['RV'].skew()\n",
    "reg_data['RV'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "原始序列的ADF检验结果:\n",
      "ADF Statistic: -3.4302\n",
      "p-value: 0.0100\n",
      "Critical Values:\n",
      "   1%: -3.4527\n",
      "   5%: -2.8714\n",
      "   10%: -2.5720\n",
      "结论: p-value小于0.05，拒绝原假设，序列是平稳的。\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller as ADF\n",
    "\n",
    "# 对月收益率数据进行ADF检验\n",
    "adf_result = ADF(reg_data[reg_data.index >= '2000-01-31']['RV'])\n",
    "\n",
    "print('原始序列的ADF检验结果:')\n",
    "print(f'ADF Statistic: {adf_result[0]:.4f}')\n",
    "print(f'p-value: {adf_result[1]:.4f}')\n",
    "print('Critical Values:')\n",
    "for key, value in adf_result[4].items():\n",
    "    print(f'   {key}: {value:.4f}')\n",
    "\n",
    "if adf_result[1] <= 0.05:\n",
    "    print('结论: p-value小于0.05，拒绝原假设，序列是平稳的。')\n",
    "else:\n",
    "    print('结论: p-value大于0.05，未能拒绝原假设，序列是非平稳的。')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS 回归结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.002\n",
      "Method:                 Least Squares   F-statistic:                    0.2224\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):              0.637\n",
      "Time:                        12:51:24   Log-Likelihood:                 390.73\n",
      "No. Observations:                 360   AIC:                            -777.5\n",
      "Df Residuals:                     358   BIC:                            -769.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0099      0.005      1.923      0.054      -0.000       0.020\n",
      "lRV           -0.2266      0.481     -0.472      0.637      -1.169       0.715\n",
      "==============================================================================\n",
      "Omnibus:                       32.778   Durbin-Watson:                   1.803\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               78.386\n",
      "Skew:                           0.448   Prob(JB):                     9.52e-18\n",
      "Kurtosis:                       5.103   Cond. No.                         97.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "model_cpi = smf.ols('ret ~ lRV',\n",
    "                 data=reg_data['1995-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从结果看，滞后一期的已实现方差（1RV）对中国股市收益率（ret）无显著解释力，该单变量模型在解释收益率波动上缺乏有效性，后续可考虑加入更多变量（如宏观经济指标、其他波动率指标等）或更换模型形式进一步分析。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.034\n",
      "Model:                            OLS   Adj. R-squared:                  0.031\n",
      "Method:                 Least Squares   F-statistic:                     7.293\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):            0.00732\n",
      "Time:                        12:51:24   Log-Likelihood:                 354.12\n",
      "No. Observations:                 300   AIC:                            -704.2\n",
      "Df Residuals:                     298   BIC:                            -696.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0213      0.007      2.874      0.004       0.007       0.036\n",
      "lcpi          -0.0073      0.003     -2.701      0.007      -0.013      -0.002\n",
      "==============================================================================\n",
      "Omnibus:                       14.234   Durbin-Watson:                   1.755\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               33.078\n",
      "Skew:                           0.111   Prob(JB):                     6.57e-08\n",
      "Kurtosis:                       4.612   Cond. No.                         4.32\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lcpi'] = reg_data['cpi'].shift(2)\n",
    "model_cpi = smf.ols('ret ~ lcpi',\n",
    "                 data=reg_data['2000-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.034\n",
      "Model:                            OLS   Adj. R-squared:                  0.028\n",
      "Method:                 Least Squares   F-statistic:                     3.773\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):             0.0241\n",
      "Time:                        12:51:24   Log-Likelihood:                 354.12\n",
      "No. Observations:                 300   AIC:                            -702.2\n",
      "Df Residuals:                     297   BIC:                            -691.1\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0212      0.008      2.611      0.009       0.005       0.037\n",
      "lRV            0.0317      1.186      0.027      0.979      -2.293       2.356\n",
      "lcpi          -0.0073      0.003     -2.718      0.007      -0.013      -0.002\n",
      "==============================================================================\n",
      "Omnibus:                       14.234   Durbin-Watson:                   1.754\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               33.202\n",
      "Skew:                           0.107   Prob(JB):                     6.17e-08\n",
      "Kurtosis:                       4.616   Cond. No.                         465.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_twovariables = smf.ols('ret ~ lRV + lcpi',\n",
    "                 data=reg_data['2000-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_twovariables.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.037\n",
      "Model:                            OLS   Adj. R-squared:                  0.027\n",
      "Method:                 Least Squares   F-statistic:                     2.581\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):             0.0537\n",
      "Time:                        12:51:24   Log-Likelihood:                 354.45\n",
      "No. Observations:                 300   AIC:                            -700.9\n",
      "Df Residuals:                     296   BIC:                            -686.1\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0826      0.088      0.937      0.349      -0.090       0.255\n",
      "lRV            0.1355      1.216      0.111      0.911      -2.249       2.520\n",
      "lpd           -0.0053      0.008     -0.696      0.487      -0.020       0.010\n",
      "lcpi          -0.0075      0.003     -2.749      0.006      -0.013      -0.002\n",
      "==============================================================================\n",
      "Omnibus:                       15.099   Durbin-Watson:                   1.746\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               35.725\n",
      "Skew:                           0.134   Prob(JB):                     1.75e-08\n",
      "Kurtosis:                       4.669   Cond. No.                     1.93e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n",
      "[2] The condition number is large, 1.93e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "reg_data['lpd'] = reg_data['pd'].shift(1)\n",
    "model3 = smf.ols('ret ~ lRV + lpd + lcpi',\n",
    "                 data=reg_data['2000-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model3.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1RV（0.1355，P=0.911）、lpd（-0.0053，P=0.487）统计不显著；lcpi（-0.0075，P=0.006）统计显著，与ret呈负向关系。0\n",
    "残差正态性检验（Jarque-Bera）显著，说明残差分布有偏差；条件数（1.93e+03）较大，提示可能存在多重共线性问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 季度结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Q</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>0.011709</td>\n",
       "      <td>0.030732</td>\n",
       "      <td>0.046608</td>\n",
       "      <td>0.058424</td>\n",
       "      <td>0.000395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>0.002337</td>\n",
       "      <td>0.005198</td>\n",
       "      <td>0.008096</td>\n",
       "      <td>0.010593</td>\n",
       "      <td>0.000014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-06-30</th>\n",
       "      <td>0.006177</td>\n",
       "      <td>0.008025</td>\n",
       "      <td>0.008207</td>\n",
       "      <td>0.010588</td>\n",
       "      <td>0.000196</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-09-30</th>\n",
       "      <td>0.119336</td>\n",
       "      <td>0.114575</td>\n",
       "      <td>0.105919</td>\n",
       "      <td>0.105381</td>\n",
       "      <td>0.000262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-12-31</th>\n",
       "      <td>0.155513</td>\n",
       "      <td>0.176020</td>\n",
       "      <td>0.199149</td>\n",
       "      <td>0.234951</td>\n",
       "      <td>0.000244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>0.003146</td>\n",
       "      <td>0.004187</td>\n",
       "      <td>0.004378</td>\n",
       "      <td>0.004791</td>\n",
       "      <td>0.000061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.009678</td>\n",
       "      <td>0.012825</td>\n",
       "      <td>0.014335</td>\n",
       "      <td>0.013999</td>\n",
       "      <td>0.000058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.004243</td>\n",
       "      <td>0.002390</td>\n",
       "      <td>0.003917</td>\n",
       "      <td>0.003171</td>\n",
       "      <td>0.000047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.015241</td>\n",
       "      <td>0.026383</td>\n",
       "      <td>0.037398</td>\n",
       "      <td>0.042365</td>\n",
       "      <td>0.000593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.017384</td>\n",
       "      <td>0.013589</td>\n",
       "      <td>0.014268</td>\n",
       "      <td>0.003617</td>\n",
       "      <td>0.000082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>137 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RV       RV1       RV2       RV3       var\n",
       "Q                                                           \n",
       "1990-12-31  0.011709  0.030732  0.046608  0.058424  0.000395\n",
       "1991-03-31  0.002337  0.005198  0.008096  0.010593  0.000014\n",
       "1991-06-30  0.006177  0.008025  0.008207  0.010588  0.000196\n",
       "1991-09-30  0.119336  0.114575  0.105919  0.105381  0.000262\n",
       "1991-12-31  0.155513  0.176020  0.199149  0.234951  0.000244\n",
       "...              ...       ...       ...       ...       ...\n",
       "2023-12-31  0.003146  0.004187  0.004378  0.004791  0.000061\n",
       "2024-03-31  0.009678  0.012825  0.014335  0.013999  0.000058\n",
       "2024-06-30  0.004243  0.002390  0.003917  0.003171  0.000047\n",
       "2024-09-30  0.015241  0.026383  0.037398  0.042365  0.000593\n",
       "2024-12-31  0.017384  0.013589  0.014268  0.003617  0.000082\n",
       "\n",
       "[137 rows x 5 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate monthly realized variance (RV) by summing squared excess returns\n",
    "Market_variance_Q = Market_ret_day.resample('QE').apply(lambda df: pd.Series({\n",
    "    'RV': (df['er']**2).sum(),\n",
    "    'RV1': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum(),\n",
    "    'RV2': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum(),\n",
    "    'RV3': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum() + 2*(df['er']*df['er3']).sum()\n",
    "}))\n",
    "\n",
    "Market_variance_Q['var'] = Market_ret_day.resample('ME')['er'].var()\n",
    "Market_variance_Q.index.name = 'month'\n",
    "\n",
    "# if RV3 <0, set to RV2 if RV2 <0, set to RV1 if RV1 <0, set to RV\n",
    "Market_variance_Q['RV1'] = Market_variance_Q['RV1'].where(Market_variance_Q['RV1']>=0, Market_variance_Q['RV'])\n",
    "Market_variance_Q['RV2'] = Market_variance_Q['RV2'].where(Market_variance_Q['RV2']>=0, Market_variance_Q['RV1'])\n",
    "Market_variance_Q['RV3'] = Market_variance_Q['RV3'].where(Market_variance_Q['RV3']>=0, Market_variance_Q['RV2'])\n",
    "Market_variance_Q.index.name = 'Q'\n",
    "Market_variance_Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RV：日超额收益（er）的平方和；\n",
    "RV1：RV基础上加入一阶交叉项（er*er1）的两倍和；\n",
    "RV2：RV1基础上加入二阶交叉项（er*er2）的两倍和；\n",
    "RV3：RV2基础上加入三阶交叉项（er*er3）的两倍和。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfqtr</th>\n",
       "      <th>cpi</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>ret</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Q</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.014687</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>6.780000e+01</td>\n",
       "      <td>11.798194</td>\n",
       "      <td>2.844483</td>\n",
       "      <td>0.866200</td>\n",
       "      <td>-0.041073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.037718</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>5.920000e+01</td>\n",
       "      <td>11.432152</td>\n",
       "      <td>2.655143</td>\n",
       "      <td>0.667672</td>\n",
       "      <td>-0.064104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.115336</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>4.440000e+01</td>\n",
       "      <td>11.317123</td>\n",
       "      <td>2.777629</td>\n",
       "      <td>0.732792</td>\n",
       "      <td>0.088951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.181765</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>3.340000e+01</td>\n",
       "      <td>11.207058</td>\n",
       "      <td>2.572886</td>\n",
       "      <td>0.556556</td>\n",
       "      <td>-0.208151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.003789</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>2.810000e+01</td>\n",
       "      <td>11.253253</td>\n",
       "      <td>2.565481</td>\n",
       "      <td>0.560128</td>\n",
       "      <td>-0.022597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.044089</td>\n",
       "      <td>0.003854</td>\n",
       "      <td>-1.000000e+00</td>\n",
       "      <td>10.817151</td>\n",
       "      <td>2.527098</td>\n",
       "      <td>0.194641</td>\n",
       "      <td>-0.047943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.010521</td>\n",
       "      <td>0.003699</td>\n",
       "      <td>-8.326673e-17</td>\n",
       "      <td>10.831573</td>\n",
       "      <td>2.559242</td>\n",
       "      <td>0.195646</td>\n",
       "      <td>0.006822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.030634</td>\n",
       "      <td>0.003604</td>\n",
       "      <td>8.000000e-01</td>\n",
       "      <td>10.770461</td>\n",
       "      <td>2.557868</td>\n",
       "      <td>0.136221</td>\n",
       "      <td>-0.034238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.159005</td>\n",
       "      <td>0.003424</td>\n",
       "      <td>1.500000e+00</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.155581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.003586</td>\n",
       "      <td>0.003358</td>\n",
       "      <td>6.000000e-01</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>0.000228</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>120 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR     rfqtr           cpi         pd        pe        pb  \\\n",
       "Q                                                                             \n",
       "1995-03-31 -0.014687  0.026386  6.780000e+01  11.798194  2.844483  0.866200   \n",
       "1995-06-30 -0.037718  0.026386  5.920000e+01  11.432152  2.655143  0.667672   \n",
       "1995-09-30  0.115336  0.026386  4.440000e+01  11.317123  2.777629  0.732792   \n",
       "1995-12-31 -0.181765  0.026386  3.340000e+01  11.207058  2.572886  0.556556   \n",
       "1996-03-31  0.003789  0.026386  2.810000e+01  11.253253  2.565481  0.560128   \n",
       "...              ...       ...           ...        ...       ...       ...   \n",
       "2023-12-31 -0.044089  0.003854 -1.000000e+00  10.817151  2.527098  0.194641   \n",
       "2024-03-31  0.010521  0.003699 -8.326673e-17  10.831573  2.559242  0.195646   \n",
       "2024-06-30 -0.030634  0.003604  8.000000e-01  10.770461  2.557868  0.136221   \n",
       "2024-09-30  0.159005  0.003424  1.500000e+00  10.889979  2.675435  0.275764   \n",
       "2024-12-31  0.003586  0.003358  6.000000e-01  10.842070  2.652927  0.261665   \n",
       "\n",
       "                 ret  \n",
       "Q                     \n",
       "1995-03-31 -0.041073  \n",
       "1995-06-30 -0.064104  \n",
       "1995-09-30  0.088951  \n",
       "1995-12-31 -0.208151  \n",
       "1996-03-31 -0.022597  \n",
       "...              ...  \n",
       "2023-12-31 -0.047943  \n",
       "2024-03-31  0.006822  \n",
       "2024-06-30 -0.034238  \n",
       "2024-09-30  0.155581  \n",
       "2024-12-31  0.000228  \n",
       "\n",
       "[120 rows x 7 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Market_ret_day复合成季收益率数据\n",
    "Q_marketret = reg_data['1995-01':'2024-12'].resample('QE').apply(\n",
    "    lambda df: pd.Series({\n",
    "        'MarketR': np.prod(1 + df['MarketR']) - 1,\n",
    "        'rfqtr': np.prod(1 + df['rfmonth']) - 1,\n",
    "        'cpi': sum(df['cpi']),\n",
    "        'pd': df['pd'].iloc[-1],\n",
    "        'pe': df['pe'].iloc[-1],\n",
    "        'pb': df['pb'].iloc[-1]\n",
    "    })\n",
    ")\n",
    "Q_marketret['ret'] = Q_marketret['MarketR'] - Q_marketret['rfqtr']\n",
    "Q_marketret.index.name = 'Q'\n",
    "Q_marketret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfqtr</th>\n",
       "      <th>cpi</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>ret</th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Q</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.014687</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>6.780000e+01</td>\n",
       "      <td>11.798194</td>\n",
       "      <td>2.844483</td>\n",
       "      <td>0.866200</td>\n",
       "      <td>-0.041073</td>\n",
       "      <td>0.035401</td>\n",
       "      <td>0.036770</td>\n",
       "      <td>0.030744</td>\n",
       "      <td>0.026817</td>\n",
       "      <td>0.000463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.037718</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>5.920000e+01</td>\n",
       "      <td>11.432152</td>\n",
       "      <td>2.655143</td>\n",
       "      <td>0.667672</td>\n",
       "      <td>-0.064104</td>\n",
       "      <td>0.165481</td>\n",
       "      <td>0.233823</td>\n",
       "      <td>0.240724</td>\n",
       "      <td>0.114255</td>\n",
       "      <td>0.000387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.115336</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>4.440000e+01</td>\n",
       "      <td>11.317123</td>\n",
       "      <td>2.777629</td>\n",
       "      <td>0.732792</td>\n",
       "      <td>0.088951</td>\n",
       "      <td>0.018665</td>\n",
       "      <td>0.016207</td>\n",
       "      <td>0.015538</td>\n",
       "      <td>0.018267</td>\n",
       "      <td>0.000157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.181765</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>3.340000e+01</td>\n",
       "      <td>11.207058</td>\n",
       "      <td>2.572886</td>\n",
       "      <td>0.556556</td>\n",
       "      <td>-0.208151</td>\n",
       "      <td>0.013791</td>\n",
       "      <td>0.008836</td>\n",
       "      <td>0.011401</td>\n",
       "      <td>0.019522</td>\n",
       "      <td>0.000153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.003789</td>\n",
       "      <td>0.026386</td>\n",
       "      <td>2.810000e+01</td>\n",
       "      <td>11.253253</td>\n",
       "      <td>2.565481</td>\n",
       "      <td>0.560128</td>\n",
       "      <td>-0.022597</td>\n",
       "      <td>0.019166</td>\n",
       "      <td>0.018851</td>\n",
       "      <td>0.009342</td>\n",
       "      <td>0.014716</td>\n",
       "      <td>0.000536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.044089</td>\n",
       "      <td>0.003854</td>\n",
       "      <td>-1.000000e+00</td>\n",
       "      <td>10.817151</td>\n",
       "      <td>2.527098</td>\n",
       "      <td>0.194641</td>\n",
       "      <td>-0.047943</td>\n",
       "      <td>0.003146</td>\n",
       "      <td>0.004187</td>\n",
       "      <td>0.004378</td>\n",
       "      <td>0.004791</td>\n",
       "      <td>0.000061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.010521</td>\n",
       "      <td>0.003699</td>\n",
       "      <td>-8.326673e-17</td>\n",
       "      <td>10.831573</td>\n",
       "      <td>2.559242</td>\n",
       "      <td>0.195646</td>\n",
       "      <td>0.006822</td>\n",
       "      <td>0.009678</td>\n",
       "      <td>0.012825</td>\n",
       "      <td>0.014335</td>\n",
       "      <td>0.013999</td>\n",
       "      <td>0.000058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.030634</td>\n",
       "      <td>0.003604</td>\n",
       "      <td>8.000000e-01</td>\n",
       "      <td>10.770461</td>\n",
       "      <td>2.557868</td>\n",
       "      <td>0.136221</td>\n",
       "      <td>-0.034238</td>\n",
       "      <td>0.004243</td>\n",
       "      <td>0.002390</td>\n",
       "      <td>0.003917</td>\n",
       "      <td>0.003171</td>\n",
       "      <td>0.000047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.159005</td>\n",
       "      <td>0.003424</td>\n",
       "      <td>1.500000e+00</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.155581</td>\n",
       "      <td>0.015241</td>\n",
       "      <td>0.026383</td>\n",
       "      <td>0.037398</td>\n",
       "      <td>0.042365</td>\n",
       "      <td>0.000593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.003586</td>\n",
       "      <td>0.003358</td>\n",
       "      <td>6.000000e-01</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>0.017384</td>\n",
       "      <td>0.013589</td>\n",
       "      <td>0.014268</td>\n",
       "      <td>0.003617</td>\n",
       "      <td>0.000082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>120 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR     rfqtr           cpi         pd        pe        pb  \\\n",
       "Q                                                                             \n",
       "1995-03-31 -0.014687  0.026386  6.780000e+01  11.798194  2.844483  0.866200   \n",
       "1995-06-30 -0.037718  0.026386  5.920000e+01  11.432152  2.655143  0.667672   \n",
       "1995-09-30  0.115336  0.026386  4.440000e+01  11.317123  2.777629  0.732792   \n",
       "1995-12-31 -0.181765  0.026386  3.340000e+01  11.207058  2.572886  0.556556   \n",
       "1996-03-31  0.003789  0.026386  2.810000e+01  11.253253  2.565481  0.560128   \n",
       "...              ...       ...           ...        ...       ...       ...   \n",
       "2023-12-31 -0.044089  0.003854 -1.000000e+00  10.817151  2.527098  0.194641   \n",
       "2024-03-31  0.010521  0.003699 -8.326673e-17  10.831573  2.559242  0.195646   \n",
       "2024-06-30 -0.030634  0.003604  8.000000e-01  10.770461  2.557868  0.136221   \n",
       "2024-09-30  0.159005  0.003424  1.500000e+00  10.889979  2.675435  0.275764   \n",
       "2024-12-31  0.003586  0.003358  6.000000e-01  10.842070  2.652927  0.261665   \n",
       "\n",
       "                 ret        RV       RV1       RV2       RV3       var  \n",
       "Q                                                                       \n",
       "1995-03-31 -0.041073  0.035401  0.036770  0.030744  0.026817  0.000463  \n",
       "1995-06-30 -0.064104  0.165481  0.233823  0.240724  0.114255  0.000387  \n",
       "1995-09-30  0.088951  0.018665  0.016207  0.015538  0.018267  0.000157  \n",
       "1995-12-31 -0.208151  0.013791  0.008836  0.011401  0.019522  0.000153  \n",
       "1996-03-31 -0.022597  0.019166  0.018851  0.009342  0.014716  0.000536  \n",
       "...              ...       ...       ...       ...       ...       ...  \n",
       "2023-12-31 -0.047943  0.003146  0.004187  0.004378  0.004791  0.000061  \n",
       "2024-03-31  0.006822  0.009678  0.012825  0.014335  0.013999  0.000058  \n",
       "2024-06-30 -0.034238  0.004243  0.002390  0.003917  0.003171  0.000047  \n",
       "2024-09-30  0.155581  0.015241  0.026383  0.037398  0.042365  0.000593  \n",
       "2024-12-31  0.000228  0.017384  0.013589  0.014268  0.003617  0.000082  \n",
       "\n",
       "[120 rows x 12 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qreg_data = pd.merge(Q_marketret,Market_variance_Q,on = 'Q')\n",
    "Qreg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the China's stock market return and inflation into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(10,5))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(Qreg_data['ret'],color='red',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='red')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(Qreg_data['RV3'].shift(1),color='blue',marker='o',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='Realized Variance')\n",
    "\n",
    "ax2.set_ylabel('Realized Variance',color='blue')\n",
    "\n",
    "plt.title('China Stock Market Return and Realized Variance')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "# save figure\n",
    "fig.savefig('images/China Stock Market Return and Realized Variance Quarter.png',dpi = 1000,bbox_inches='tight')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "股市收益率（红色）与已实现方差（蓝色）在部分时段呈现反向波动（如 1997 年、2015 年附近），体现 “高波动伴随收益波动” 的市场特征；但整体联动规律不绝对，说明市场收益与风险的关系存在复杂性。\n",
    "1997 年、2008 年、2015 年等时段，两者均出现显著峰值，对应亚洲金融危机、全球金融危机、国内股市异动等事件，验证了已实现方差对市场冲击的敏感性。\n",
    "季度维度的双轴图能直观展现长期内收益与风险的动态关系，为跨周期的市场分析、资产配置提供视觉化的实证支持。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "================================================================================\n",
      "Model with lRV:\n",
      "================================================================================\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                  0.003\n",
      "Method:                 Least Squares   F-statistic:                     1.070\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):              0.303\n",
      "Time:                        12:51:26   Log-Likelihood:                 46.659\n",
      "No. Observations:                 119   AIC:                            -89.32\n",
      "Df Residuals:                     117   BIC:                            -83.76\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0135      0.017      0.782      0.434      -0.020       0.048\n",
      "lRV            0.8117      0.785      1.034      0.301      -0.726       2.350\n",
      "==============================================================================\n",
      "Omnibus:                       17.209   Durbin-Watson:                   1.636\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               21.299\n",
      "Skew:                           0.816   Prob(JB):                     2.37e-05\n",
      "Kurtosis:                       4.277   Cond. No.                         45.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n",
      "\n",
      "================================================================================\n",
      "Model with lRV1:\n",
      "================================================================================\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.012\n",
      "Model:                            OLS   Adj. R-squared:                  0.003\n",
      "Method:                 Least Squares   F-statistic:                     1.338\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):              0.250\n",
      "Time:                        12:51:26   Log-Likelihood:                 46.656\n",
      "No. Observations:                 119   AIC:                            -89.31\n",
      "Df Residuals:                     117   BIC:                            -83.75\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0159      0.016      0.966      0.334      -0.016       0.048\n",
      "lRV1           0.6284      0.543      1.157      0.247      -0.436       1.693\n",
      "==============================================================================\n",
      "Omnibus:                       17.808   Durbin-Watson:                   1.633\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               22.204\n",
      "Skew:                           0.838   Prob(JB):                     1.51e-05\n",
      "Kurtosis:                       4.292   Cond. No.                         35.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n",
      "\n",
      "================================================================================\n",
      "Model with lRV2:\n",
      "================================================================================\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.031\n",
      "Model:                            OLS   Adj. R-squared:                  0.022\n",
      "Method:                 Least Squares   F-statistic:                     2.826\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):             0.0954\n",
      "Time:                        12:51:26   Log-Likelihood:                 47.798\n",
      "No. Observations:                 119   AIC:                            -91.60\n",
      "Df Residuals:                     117   BIC:                            -86.04\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0088      0.017      0.526      0.599      -0.024       0.042\n",
      "lRV2           0.9907      0.589      1.681      0.093      -0.164       2.146\n",
      "==============================================================================\n",
      "Omnibus:                       18.124   Durbin-Watson:                   1.623\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               23.305\n",
      "Skew:                           0.830   Prob(JB):                     8.70e-06\n",
      "Kurtosis:                       4.395   Cond. No.                         34.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n",
      "\n",
      "================================================================================\n",
      "Model with lRV3:\n",
      "================================================================================\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.050\n",
      "Model:                            OLS   Adj. R-squared:                  0.042\n",
      "Method:                 Least Squares   F-statistic:                     4.607\n",
      "Date:                Mon, 20 Oct 2025   Prob (F-statistic):             0.0339\n",
      "Time:                        12:51:26   Log-Likelihood:                 48.998\n",
      "No. Observations:                 119   AIC:                            -94.00\n",
      "Df Residuals:                     117   BIC:                            -88.44\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0021      0.018     -0.121      0.903      -0.037       0.032\n",
      "lRV3           1.5009      0.699      2.146      0.032       0.130       2.871\n",
      "==============================================================================\n",
      "Omnibus:                       16.681   Durbin-Watson:                   1.645\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               22.499\n",
      "Skew:                           0.738   Prob(JB):                     1.30e-05\n",
      "Kurtosis:                       4.535   Cond. No.                         40.9\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "Qreg_data['lRV'] = Qreg_data['RV'].shift(1)\n",
    "Qreg_data['lRV1'] = Qreg_data['RV1'].shift(1)\n",
    "Qreg_data['lRV2'] = Qreg_data['RV2'].shift(1)\n",
    "Qreg_data['lRV3'] = Qreg_data['RV3'].shift(1)\n",
    "model_qrv = smf.ols('ret ~ lRV',\n",
    "                 data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model_qrv1 = smf.ols('ret ~ lRV1',\n",
    "                 data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model_qrv2 = smf.ols('ret ~ lRV2',\n",
    "                 data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model_qrv3 = smf.ols('ret ~ lRV3',\n",
    "                 data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "\n",
    "# print all model summaries together\n",
    "print(\"=\" * 80)\n",
    "print(\"Model with lRV:\")\n",
    "print(\"=\" * 80)\n",
    "print(model_qrv.summary())\n",
    "print(\"\\n\" + \"=\" * 80)\n",
    "print(\"Model with lRV1:\")\n",
    "print(\"=\" * 80)\n",
    "print(model_qrv1.summary())\n",
    "print(\"\\n\" + \"=\" * 80)\n",
    "print(\"Model with lRV2:\")\n",
    "print(\"=\" * 80)\n",
    "print(model_qrv2.summary())\n",
    "print(\"\\n\" + \"=\" * 80)\n",
    "print(\"Model with lRV3:\")\n",
    "print(\"=\" * 80)\n",
    "print(model_qrv3.summary())\n",
    "# print all model summaries together\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1RV与ret呈正向关系，但 P 值（0.301）远大于 0.05，系数统计不显著。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "回归结果对比分析<br><table style=\"text-align:center\"><tr><td colspan=\"5\" style=\"border-bottom: 1px solid black\"></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td colspan=\"4\"><em>Dependent variable: ret</em></td></tr><tr><td style=\"text-align:left\"></td><tr><td></td><td colspan=\"1\">模型一</td><td colspan=\"1\">模型二</td><td colspan=\"1\">模型三</td><td colspan=\"1\">模型四</td></tr>\n",
       "<tr><td colspan=\"5\" style=\"border-bottom: 1px solid black\"></td></tr>\n",
       "\n",
       "<tr><td style=\"text-align:left\">Intercept</td><td>0.014<sup></sup></td><td>0.016<sup></sup></td><td>0.009<sup></sup></td><td>-0.002<sup></sup></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td>(0.017)</td><td>(0.016)</td><td>(0.017)</td><td>(0.018)</td></tr>\n",
       "<tr><td style=\"text-align:left\">lRV</td><td>0.812<sup></sup></td><td></td><td></td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td>(0.785)</td><td></td><td></td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\">lRV1</td><td></td><td>0.628<sup></sup></td><td></td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td></td><td>(0.543)</td><td></td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\">lRV2</td><td></td><td></td><td>0.991<sup>*</sup></td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td></td><td></td><td>(0.589)</td><td></td></tr>\n",
       "<tr><td style=\"text-align:left\">lRV3</td><td></td><td></td><td></td><td>1.501<sup>**</sup></td></tr>\n",
       "<tr><td style=\"text-align:left\"></td><td></td><td></td><td></td><td>(0.699)</td></tr>\n",
       "\n",
       "<td colspan=\"5\" style=\"border-bottom: 1px solid black\"></td></tr>\n",
       "<tr><td style=\"text-align: left\">Observations</td><td>119</td><td>119</td><td>119</td><td>119</td></tr><tr><td style=\"text-align: left\">R<sup>2</sup></td><td>0.012</td><td>0.012</td><td>0.031</td><td>0.050</td></tr><tr><td style=\"text-align: left\">Adjusted R<sup>2</sup></td><td>0.003</td><td>0.003</td><td>0.022</td><td>0.042</td></tr><tr><td style=\"text-align: left\">Residual Std. Error</td><td>0.165 (df=117)</td><td>0.165 (df=117)</td><td>0.163 (df=117)</td><td>0.162 (df=117)</td></tr><tr><td style=\"text-align: left\">F Statistic</td><td>1.070<sup></sup> (df=1; 117)</td><td>1.338<sup></sup> (df=1; 117)</td><td>2.826<sup>*</sup> (df=1; 117)</td><td>4.607<sup>**</sup> (df=1; 117)</td></tr>\n",
       "<tr><td colspan=\"5\" style=\"border-bottom: 1px solid black\"></td></tr><tr><td style=\"text-align: left\">Note:</td><td colspan=\"4\" style=\"text-align: right\"><sup>*</sup>p&lt;0.1; <sup>**</sup>p&lt;0.05; <sup>***</sup>p&lt;0.01</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from stargazer.stargazer import Stargazer\n",
    "from IPython.core.display import HTML\n",
    "\n",
    "stargazer = Stargazer([model_qrv, model_qrv1, model_qrv2, model_qrv3])\n",
    "stargazer.title(\"回归结果对比分析\")\n",
    "stargazer.custom_columns(['模型一', '模型二', '模型三', '模型四'])\n",
    "stargazer.show_model_numbers(False)\n",
    "stargazer.show_confidence_intervals(False)\n",
    "\n",
    "# 生成HTML格式\n",
    "html_output = stargazer.render_html()\n",
    "HTML(html_output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "仅IRV3在 5% 显著性水平下（**）对ret有正向影响；IRV、IRV1、IRV2系数均不显著。\n",
    "四个模型的 R² 均低于 0.05，调整后 R² 也极低，说明即使IRV3显著，整体模型对收益率波动的解释力仍很弱。\n",
    "所有模型观测数均为 119，残差标准误差异较小；F 统计量仅模型四（4.607**）显著，说明只有纳入IRV3的模型整体边际显著。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " 使用 statsmodels 的 summary_col（显示t值）\n",
      "\n",
      "\n",
      "==============================================\n",
      "                  RV     RV1     RV2     RV3  \n",
      "----------------------------------------------\n",
      "Intercept      0.014   0.016   0.009   -0.002 \n",
      "               (0.017) (0.016) (0.017) (0.018)\n",
      "lRV            0.812                          \n",
      "               (0.785)                        \n",
      "lRV1                   0.628                  \n",
      "                       (0.543)                \n",
      "lRV2                           0.991*         \n",
      "                               (0.589)        \n",
      "lRV3                                   1.501**\n",
      "                                       (0.699)\n",
      "R-squared      0.012   0.012   0.031   0.050  \n",
      "R-squared Adj. 0.003   0.003   0.022   0.042  \n",
      "N              119     119     119     119    \n",
      "==============================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "# 使用 summary_col 进行多模型对比（推荐用于Jupyter）\n",
    "from statsmodels.iolib.summary2 import summary_col\n",
    "\n",
    "# 创建对比表\n",
    "results_table = summary_col(\n",
    "    [model_qrv, model_qrv1, model_qrv2, model_qrv3],\n",
    "    model_names=['RV', 'RV1', 'RV2', 'RV3'],\n",
    "    stars=True,\n",
    "    float_format='%.3f',\n",
    "    info_dict={\n",
    "        'N': lambda x: f\"{int(x.nobs)}\"\n",
    "    }\n",
    ")\n",
    "\n",
    "print(\"\\n 使用 statsmodels 的 summary_col（显示t值）\\n\")\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "仅IRV3在 5% 显著性水平下（**）对ret有正向影响；IRV、IRV1、IRV2系数均不显著。\n",
    "四个模型的 R-squared 均低于 0.06，调整后 R-squared 也极低，说明即使IRV3显著，整体模型对收益率波动的解释力仍很弱。\n",
    "所有模型观测数均为 119，残差标准误等统计量差异较小，保证了模型间对比的一致性。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 波动率和价格比率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "======================================\n",
      "                 PB模型    PE模型    PD模型 \n",
      "--------------------------------------\n",
      "Intercept      0.045   0.130   0.261  \n",
      "               (0.034) (0.104) (0.292)\n",
      "lRV            1.299   1.059   1.054  \n",
      "               (1.429) (1.483) (1.461)\n",
      "lpb            -0.058                 \n",
      "               (0.041)                \n",
      "lpe                    -0.042         \n",
      "                       (0.035)        \n",
      "lpd                            -0.022 \n",
      "                               (0.026)\n",
      "R-squared      0.032   0.024   0.019  \n",
      "R-squared Adj. 0.012   0.004   -0.002 \n",
      "N              100     100     100    \n",
      "======================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "Qreg_data['lpd'] = Qreg_data['pd'].shift(1)\n",
    "Qreg_data['lpb'] = Qreg_data['pb'].shift(1)\n",
    "Qreg_data['lpe'] = Qreg_data['pe'].shift(1)\n",
    "model1 = smf.ols('ret ~ lRV + lpb',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model2 = smf.ols('ret ~ lRV + lpe',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model3 = smf.ols('ret ~ lRV + lpd',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "\n",
    "# 创建对比表\n",
    "results_table = summary_col(\n",
    "    [model1, model2, model3],\n",
    "    model_names=['PB模型', 'PE模型', 'PD模型'],\n",
    "    stars=True,\n",
    "    float_format='%.3f',\n",
    "    info_dict={\n",
    "        'N': lambda x: f\"{int(x.nobs)}\"\n",
    "    }\n",
    ")\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "===============================================\n",
      "                 RV3      PB       PE      PD  \n",
      "-----------------------------------------------\n",
      "Intercept      -0.002  0.044*   0.151*  0.277  \n",
      "               (0.018) (0.027)  (0.082) (0.190)\n",
      "lRV3           1.501** 1.808*** 1.674** 1.641**\n",
      "               (0.699) (0.699)  (0.719) (0.710)\n",
      "lpb                    -0.065**                \n",
      "                       (0.030)                 \n",
      "lpe                             -0.052*        \n",
      "                                (0.027)        \n",
      "lpd                                     -0.024 \n",
      "                                        (0.017)\n",
      "R-squared      0.050   0.078    0.071   0.062  \n",
      "R-squared Adj. 0.042   0.062    0.055   0.046  \n",
      "N              119     119      119     119    \n",
      "===============================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols('ret ~ lRV3',\n",
    "                    data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model1 = smf.ols('ret ~ lRV3 + lpb',\n",
    "                    data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model2 = smf.ols('ret ~ lRV3 + lpe',\n",
    "                    data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model3 = smf.ols('ret ~ lRV3 + lpd',\n",
    "                    data=Qreg_data['1995-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "\n",
    "# 创建对比表\n",
    "results_table = summary_col(\n",
    "    [model, model1, model2, model3],\n",
    "    model_names=['RV3', 'PB', 'PE', 'PD'],\n",
    "    stars=True,\n",
    "    float_format='%.3f',\n",
    "    info_dict={\n",
    "        'N': lambda x: f\"{int(x.nobs)}\"\n",
    "    }\n",
    ")\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "IRV3在所有模型中均在 5% 显著性水平下（**）对ret有正向影响；lpb（**）负向显著，lpe（*）负向显著，lpd不显著。\n",
    "加入估值指标后，模型的 R-squared 和调整后 R-squared 均有提升（如model1的 R-squared 为 0.078），说明估值指标能增强模型对收益率的解释力。\n",
    "所有模型观测数均为 119，保证了模型间对比的一致性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "======================================================================================\n",
      "                 RV3      PB      PE      PD      CPI      PB+CPI    PE+CPI    PD+CPI \n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept      -0.004  0.039   0.135   0.295   0.038     0.083**   0.257**   0.484*   \n",
      "               (0.020) (0.032) (0.098) (0.289) (0.029)   (0.037)   (0.110)   (0.266)  \n",
      "lRV3           1.530   1.925   1.710   1.693   2.075**   2.496**   2.433**   2.366**  \n",
      "               (1.242) (1.210) (1.248) (1.227) (1.035)   (1.063)   (1.077)   (1.075)  \n",
      "lpb                    -0.067*                           -0.070**                     \n",
      "                       (0.039)                           (0.035)                      \n",
      "lpe                            -0.048                              -0.073**           \n",
      "                               (0.033)                             (0.034)            \n",
      "lpd                                    -0.026                                -0.039*  \n",
      "                                       (0.025)                               (0.023)  \n",
      "lcpi                                           -0.008*** -0.009*** -0.010*** -0.009***\n",
      "                                               (0.003)   (0.003)   (0.003)   (0.003)  \n",
      "R-squared      0.036   0.067   0.056   0.049   0.129     0.162     0.173     0.157    \n",
      "R-squared Adj. 0.026   0.047   0.036   0.029   0.111     0.136     0.147     0.130    \n",
      "N              100     100     100     100     100       100       100       100      \n",
      "======================================================================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "Qreg_data['lcpi'] = Qreg_data['cpi'].shift(1)\n",
    "model = smf.ols('ret ~ lRV3',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model1 = smf.ols('ret ~ lRV3 + lpb',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model2 = smf.ols('ret ~ lRV3 + lpe',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model3 = smf.ols('ret ~ lRV3 + lpd',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "\n",
    "model4 = smf.ols('ret ~ lRV3 + lcpi',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model5 = smf.ols('ret ~ lRV3 + lpb + lcpi',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model6 = smf.ols('ret ~ lRV3 + lpe + lcpi',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "model7 = smf.ols('ret ~ lRV3 + lpd + lcpi',\n",
    "                    data=Qreg_data['2000-01':'2024-12']).fit(\n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "\n",
    "# 创建对比表\n",
    "results_table = summary_col(\n",
    "    [model, model1, model2, model3, model4, model5, model6, model7],\n",
    "    model_names=['RV3', 'PB', 'PE', 'PD', 'CPI', 'PB+CPI', 'PE+CPI', 'PD+CPI'],\n",
    "    stars=True,\n",
    "    float_format='%.3f',\n",
    "    info_dict={\n",
    "        'N': lambda x: f\"{int(x.nobs)}\"\n",
    "    }\n",
    ")\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 模型构建逻辑\n",
    "核心自变量：以IRV3为基础，分别加入滞后市净率（lpb）、滞后市盈率（lpe）、滞后股息价格比（lpd）、滞后通胀（lcpi），以及它们的组合（如lpb+lcpi、lpe+lcpi、lpd+lcpi），构建 8 个 OLS 模型。\n",
    "数据范围与方法：选取 2000 年 1 月至 2024 年 12 月的数据，采用 HAC（异方差自相关一致）协方差估计，最大滞后阶数为 2。\n",
    "2. 多模型对比设计\n",
    "通过summary_col工具将 8 个模型整合为对比表格，模型命名为 “RV3”“PB”“PE”“PD”“CPI”“PB+CPI”“PE+CPI”“PD+CPI”，并标注显著性水平（*p<0.1；**p<0.05；***p<0.01），同时统计观测数（N）。"
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